Triangular prism (EntityTopic, 20)

(Redirected from Rotope 8)

The triangular prism is the prism whose base is a triangle. If the sides are squares, it is a uniform polyhedron.

Coordinates

The coordinates of a triangular prism of side 2 are:

(±1, -√3/3, ±1)
(0, 2√3/3, ±1)

Equations

• Variables:
l ⇒ length of edges of triangular prism
total edge length = 9l
surface area = (3 + √32) · l2
volume = √34 · l3
[!x,!y] ⇒ square [!z] ⇒ triangle

Incidence matrix

Dual: triangular bipyramid

 # TXID Type Name Va Ea Eb 4a 3a 0 Va = point ; 1 Ea 2 = digon ; 2 Eb 2 = digon ; 3 4a 4 2 2 = square ; 4 3a 3 0 3 = base of prism: triangle ; 5 C1a 6 3 6 3 2 = triangular prism ;

Usage as facets

 Notable Trishapes Regular: tetrahedron • cube • octahedron • dodecahedron • icosahedron Direct truncates: tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate Mesotruncates: stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron Snubs: snub staurohedron • snub rhodohedron Curved: sphere • torus • cylinder • cone • frustum • crind

 9. [11]1Square pyramid 10. 111Triangular prism 11. 12Tetrahedron List of tapertopes